Calculus Examples

Evaluate the Integral integral of 4sin(x)^2 with respect to x
Step 1
Since is constant with respect to , move out of the integral.
Step 2
Use the half-angle formula to rewrite as .
Step 3
Since is constant with respect to , move out of the integral.
Step 4
Simplify.
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Step 4.1
Combine and .
Step 4.2
Cancel the common factor of and .
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Step 4.2.1
Factor out of .
Step 4.2.2
Cancel the common factors.
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Step 4.2.2.1
Factor out of .
Step 4.2.2.2
Cancel the common factor.
Step 4.2.2.3
Rewrite the expression.
Step 4.2.2.4
Divide by .
Step 5
Split the single integral into multiple integrals.
Step 6
Apply the constant rule.
Step 7
Since is constant with respect to , move out of the integral.
Step 8
Let . Then , so . Rewrite using and .
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Step 8.1
Let . Find .
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Step 8.1.1
Differentiate .
Step 8.1.2
Since is constant with respect to , the derivative of with respect to is .
Step 8.1.3
Differentiate using the Power Rule which states that is where .
Step 8.1.4
Multiply by .
Step 8.2
Rewrite the problem using and .
Step 9
Combine and .
Step 10
Since is constant with respect to , move out of the integral.
Step 11
The integral of with respect to is .
Step 12
Simplify.
Step 13
Replace all occurrences of with .
Step 14
Simplify.
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Step 14.1
Combine and .
Step 14.2
Apply the distributive property.
Step 14.3
Cancel the common factor of .
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Step 14.3.1
Move the leading negative in into the numerator.
Step 14.3.2
Cancel the common factor.
Step 14.3.3
Rewrite the expression.